Electrons are accelerated through a potential difference V and protons are accelerated through a potential difference 4 ~V . The de-Broglie wavelengths are _e and _p for electrons and protons respectively. The ratio of _e _p is given by: (given m_e is mass of electron and m_p is mass of proton).

Step-by-step solution

Energy in joule (E) = charge potential diff. in volt E _ electron = q _ c V and E _ proton = q _ p 4 ~V de-Broglie wavelength = h P = h 2 mE array r _ e = h 2 ~m _ e eV and _ P = h 2 ~m _ e e 4 ~V ( q _ e = q _ P ) array aligned _ e _ P & = h 2 ~m _ e eV h 2 ~m _ P e 4 ~V = 2 ~m _ P e 4 ~V 2 ~m _ e eV & =2 m _ P m _ e aligned